How do I graph an absolute value inequality in 2 variables?

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Discussion Overview

The discussion revolves around the process of graphing absolute value inequalities in two variables. Participants share methods and tools for visualizing these inequalities, focusing on breaking down the problem into manageable parts.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant expresses difficulty in understanding how to graph an absolute value inequality despite being familiar with its appearance on a graphing calculator.
  • Another participant suggests breaking the problem into three regions based on the value of x: x < -1, -1 <= x <= 1, and x > 1, and then deriving linear functions for each region.
  • A further contribution outlines a step-by-step algorithm for handling absolute value problems, including determining zeros, simplifying expressions within each region, and iterating through intervals.
  • One participant recommends using an online tool, webgraphing.com, for plotting inequalities in two variables, specifically mentioning how to represent absolute values in the tool.

Areas of Agreement / Disagreement

Participants present various methods and tools for graphing absolute value inequalities, but there is no consensus on a single approach or resolution to the initial question.

Contextual Notes

Some methods depend on the specific form of the absolute value inequality, and the effectiveness of the suggested online tool may vary based on user familiarity with it.

Who May Find This Useful

Students and individuals seeking assistance with graphing absolute value inequalities, particularly in a two-variable context.

Triggy
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I need some help graphing an Absolute value. I know what it look like from a graphing calculator but I don't understand how to get to the answer.

http://media.twango.com/m1/original/0042/5fda15431b96400eb32e66afa3627624.jpg

Thanks
 
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With one like that the best method is to break it into regions. Just get a simple linear function for each of the following three regions and you're done.

1. x < -1
2. -1 <= x <= 1
3. x > 1
 
Following uart, adhere to this algorithm when doing abs.val problems:
1. Determine the zeros of each absolute value term, and mark these off on a number line.
2.Within each region, every absolute value term is now easily converted into a non-absolute-alue term
3. Simplify the expresion you have gotten for each interval, and draw that portion of the graph.
4. Iterate with the next region.
 
graphing inequalities in 2 variables

Triggy,

You can plot your inequality on www.webgraphing.com. There, you will get both the plot of the curve and the region where the inequality holds. Just use the link to "Inequality Graphing in Two Variables." To represent |x|, use the notation abs(x).
 

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